We work as well with various notions of the “category of spectra”. In the first part of subsec:shadows, we consider a monoidal model category of spectra, denoted \(\mathcal {S}p\) , e.g., symmetric spectra or orthogonal spectra [1]}. We denote the monoidal product on \(\mathcal {S}p\)  by \(\wedge \) . We let \(\mathrm {Sp}\)  denote the \(\infty \) -category of spectra and \(\mathrm {Ho}(\mathrm {Sp})\)  its homotopy category, which is equivalent to the homotopy category of the model category \(\mathcal {S}p\) .
